Part 7

While these bullets were making, the thermometer exposed to the open air was at the freezing point, or some degrees below; but in the pit where the bullets were suffered to cool, the thermometer was nearly ten degrees above that point; that is to say, to the degree of temperature of the pits of the observatory, and it is this degree which I have here taken for that of the actual temperature of the earth. To know the exact moment of their cooling to this actual temperature, other bullets of the same matters, diameters, and not heated, were made use of for comparison, and which were felt at the same time as the others. By the immediate touch of the hand, or two hands, on the two bullets, we could judge of the moment when they were equally cold; and as the greater or less smoothness or roughness of bodies makes a great difference to the touch; (a smooth body, whether hot or cold, appearing much more so than a rough body, even of the same matter, although they are both equally so) I took care that the cold bullets were rough, and like those which had been heated, whose surfaces were sprinkled over with little eminences produced by the fire.

EXPERIMENTS.

I. The bullet of half an inch was heated white in two minutes, cooled so as to be held in the hand in 12, and to the actual temperature in 39 minutes.

II. That of an inch, heated white in five minutes and a half, cooled so as to be held in the hand, in 35-1/2 minutes, and to the actual temperature in one hour and 23 minutes.

III. That of an inch and an half, heated white in nine minutes, cooled so as to be held in the hand in 58 minutes, and to the actual temperature in two hours and 35 minutes.

IV. That of two inches heated white in 13 minutes, cooled so as to be held in the hand in one hour 20 minutes, and to the actual temperature in three hours 16 minutes.

V. That bullet of two inches and an half heated white in 16 minutes, cooled so as to be held in the hand in one hour 42 minutes, and to the actual temperature in four hours 30 minutes.

VI. That bullet of three inches heated white in 19-1/2 minutes, cooled so as to be held in the hand in two hours seven minutes, and to the actual temperature in five hours eight minutes.

VII. That of three inches and a half heated white in 23-1/2 minutes, cooled so as to be held in the hand in two hours 36 minutes, and to the actual temperature in five hours 56 minutes.

VIII. That of four inches heated white in 27 minutes and a half, cooled so as to be held in the hand in three hours two minutes, and to the actual temperature in six hours 55 minutes.

IX. That of four inches and a half heated white in 31 minutes, cooled so as to be held in the hand in three hours and 25 minutes, and to the actual temperature in seven hours 46 minutes.

X. That of five inches heated white in 34 minutes, cooled, so as to be held in the hand, in three hours 52 minutes, and to the actual temperature in eight hours 42 minutes.

The most constant difference that can be taken between each of the terms which express the time of cooling, from the instant the bullets were drawn from the fire, to that when we can touch them unhurt, is found to be about 24 minutes, for, by supposing each term to increase 24, we shall have 12, 36, 60, 84, 108, 132, 156, 180, 204, 228 minutes. And the continuation of the real time of these coolings are, 12, 35-1/2, 58, 80, 102, 127, 156, 182, 205, 232 minutes, which approach the first as nearly as experiment can approach calculation.

So, likewise, the most constant difference to be found between each of the terms of cooling to actual temperature is found to be 54 minutes, for by supposing each term to increase 54, we shall have 39, 93, 147, 201, 255, 309, 363, 417, 471, 525 minutes, and the continuation of the real time of this cooling is found, by the preceding experiments, to be 39, 93, 145, 196, 248, 308, 356, 415, 466, 522 minutes, which approaches also nearest to the first.

I made the like experiments upon the same bullets twice or thrice, but found I could only rely on the first, because each time the bullets were heated they lost a considerable part of their weight, which was occasioned not only by the falling off of the parts of the surface reduced into scoria, but also by a kind of drying, or internal calcination, which diminishes the weight of the constituent parts, insomuch that it appears a strong fire renders the iron specifically lighter each time it is heated; and I have found, by subsequent experiments, that this diminution of weight varies much, according to the different quality of the iron. Experience has also confirmed me in the opinion, that the duration of heat, or the time taken up in cooling of iron, is not in a smaller, as stated in a passage of Newton, but in a larger ratio than that of the diameter.

Now if we would enquire how long it would require for a globe as large as the earth to cool, we should find, after the preceding experiments, that instead of 50,000 years, which Newton assigns for the earth to cool to the present temperature, it would take 42,964 years, 221 days, to cool only to the point where it would cease to burn, and 86,667 years and 132 days, to cool to the present temperature.

It might only be supposed, that the refrigeration of the earth should be considerably increased, because we imagine that refrigeration is performed by the contact of the air, and that there is a great difference between the time of refrigeration in the air and in vacuo; and supposing that the earth and air cool in the same time in vacuo, this surplus of time should be reckoned. But, in fact, this difference of time is very inconsiderable, for though the density of the medium, in which a body cools, makes something on the duration of the refrigeration, yet this effect is much less than might be imagined, since in mercury, which is eleven thousand times denser than air, it is only requisite to plunge bodies into it about nine times as often as is required to produce the same refrigeration in air. The principal cause of refrigeration is not, therefore, the contact of the ambient medium, but the expansive force which animates the parts of heat and fire, which drives them out of the bodies wherein they reside, and impels them directly from the centre to the circumference.

By comparing the time employed in the preceding experiments to heat the iron globes, with that requisite to cool them, we find that they may be heated till they become white in one sixth part and a half of the time they take to cool, so as to be held in the hand, and about one fifteenth and a half of that to cool to actual temperature, so that there is a great error in the estimate which Newton made on the heat communicated by the sun to the comet of 1680, for that comet having been exposed to the violent heat of the sun but a short time, could receive it only in proportion thereto, and not only in so great a degree as that author supposes. Indeed, in the passage alluded to, he considers the heat of red-hot iron much less than in fact it is, and he himself states it to be, in a Memoir, entitled, _The Scale of Heat_, published in the Philosophical Transactions of 1701, which was many years after the publication of his _principles_. We see in that excellent Memoir, which includes the germ of all the ideas on which thermometers have since been constructed; that Newton, after very exact experiments, makes the heat of boiling water to be three times greater than that of the sun in the height of summer; that of melted tin, six times greater; that of melted lead, eight times; that of melted regulus, twelve times; and that of a common culinary fire, sixteen or seventeen times; hence we may conclude, that the heat of iron, when heated so as to become white, is still greater, since it requires a fire continually animated by the bellows to heat it to that degree. Newton seems to be sensible of this, for he says, that the heat of iron in that state seems to be seven or eight times greater than that of boiling water. This diminishes half the heat of this comet, compared to that of hot iron.

But this diminution, which is only relative, is nothing in itself, nor nothing in comparison with that real and very great diminution which results from our first consideration. For the comet to have received this heat a thousand times greater than that of red-hot iron, it must have remained a very long time in the vicinity of the sun, whereas it only passed very rapidly at a small distance. It was on the 8th of December, 1680, at 6/1000 distance from the earth to the centre of the sun; but 24 hours before, and as many after, it was at a distance six times greater, and where the heat was consequently 36 times less.

To know then the quantity of this heat communicated to the comet by the sun, we here find how we should make this estimation tolerably just, and, at the same time, make the comparison with hot iron by the means of my experiments.

We shall suppose, as a fact, that this comet took up 666 hours to descend from the point where it then was, and which point was at an equal distance as the earth is from the sun, consequently it received an equal heat to what the earth receives from that luminary, and which I here take for unity; we shall likewise suppose that the comet took 666 hours more to ascend from the lowest point of its perihelium to this same distance; and supposing also its motion uniform, we shall perceive, that the comet being at the lowest point of its perihelium, that is, to 6/1000 of the distance from the earth to the sun, the heat it received in that motion was 27,766 times greater than that the earth receives. By giving to this motion a duration of 80 minutes, viz. 40 for its descent, and 40 for its ascent, we shall have, at 6 distance, 27,776 heat during 80 minutes at 7 distance 20,408 heat also during 80 minutes, and at 8 distance 15,625 heat during 80 minutes, and thus, successively, to the distance of 1000, where the heat is one. By summing up the quantity of heat at each distance we shall find 363,410 to be the total of the heat the comet has received from the sun, as much in descending as in ascending, which must be multiplied by the time, that is, by four thirds of an hour; we shall then have 484,547, which divided by 2,000 represents the solid heat the earth received in this time of 1332 hours, since the distance is always 1,300, and the heat always equals one. Thus we shall have 242,547/2000 for the heat the comet received more than the earth during the whole time of its perihelium instead of 28,000, as Newton supposed it, because he took only the extreme point, and paid no attention to the very small duration of time. And this heat must still be diminished 242,547/2000, because the comet ran, by its acceleration, as much more way in the same as it was nearer the sun. But by neglecting this diminution, and admitting that the comet received a heat nearly 242 times greater than that of our summer's sun, and, consequently 17-2/7 times greater than that of hot iron, according to Newton's estimation, or only ten minutes greater according to this estimation; it must be supposed, that give a heat ten times greater than that of red hot iron, it required ten times more time; that is to say, 1332; consequently, we may compare the comet to a globe of iron heated by a forge fire for 13320 hours, to heat it to a whiteness.

Now we find by calculation from my experiments, that with a forge fire, we can heat to a whiteness a globe whose diameter is 228342-1/2 inches in 799200 minutes, and, consequently, the whole mass of the comet to be heated to the point of iron to a whiteness, during the short time it was exposed to the heat of the sun, could only be 223342-1/2 inches in diameter; and even then it must have been struck on all sides, and at the same time, by the light of the sun. Thus comets, when they approach the sun, do not receive an immense nor a very durable heat, as Newton says, and as we at the first view might be inclined to believe. Their stay is so short in the vicinity of the sun, that their masses have not time to be heated, and besides only part of their surface is exposed to it; this part is burnt by the extreme heat, which by calcining and volatilizing the matter of this surface, drives it outwardly in vapours and dust from the opposite side to the sun; and what is called the tail of the comet, is nothing else than the light of the sun rendered visible, as in a dark room, by those atoms which the heat lengthens as it is more violent.

But another consideration very different and infinitely more important, is, that to apply the result of our experiments and calculation to the comet and earth, we must suppose them composed of matters which would demand as much time as iron to cool: whereas, in reality, the principal matters of which the terrestrial globe is composed, such as clay, stones, &c. cannot possibly take so long.

To satisfy myself on this point, I caused globes of clay and marl to be made, and having heated them at the same forge until white, I found that the clay balls of two inches, cooled in 38 minutes so as to be held in the hand; those of two inches and an half, in 48 minutes; and those of three inches, in 60 minutes; which being compared with the time of the refrigeration of iron bullets of the same diameters, give 38 to 80 for two inches, 48 to 102 for two inches and a half, and 60 to 127 for three inches; so that only half the time is required for the refrigeration of clay, to what is necessary for iron.

I found also, that lumps of clay, or marl, of two inches, refrigerated so as to be held in the hand in 45 minutes; those of two inches and a half in 58; and those of three inches in 75, which being compared with the time of refrigeration of iron bullets of the same diameters, gives 46 to 80 for two inches, 58 to 102 for two inches and a half, and 75 to 127 for three inches, which nearly form the ratio of 9 to 5; so that for the refrigeration of clay, more than half the time is required than for iron.

It is necessary to observe, that globes of clay heated white, lost more of their weight than iron bullets, even to the ninth or tenth part of their weight: whereas marl heated in the same fire, lost scarcely any thing, although the whole surface was covered over with scales, and reduced into glass. As this appeared singular, I repeated the experiment several times, increasing the fire, and continuing it longer than for iron; and although it scarcely required a third of the time to redden marl, to what it did to redden iron, I kept them in the fire thrice as long as was requisite, to see if they would lose more, but I found very trifling diminutions; for the globe of two inches heated for eight minutes, which weighed seven ounces, two drachms, and thirty grains, before it was put in the fire, lost only forty-one grains, which does not make a hundredth part of its weight; and that of three inches, which weighed twenty-four ounces, five drachms, and thirteen grains, having been heated by the fire for eighteen minutes, that is nearly as much as iron, lost only seventy-eight grains, which does not make the hundredth and eighty-first part of its weight. These losses are so trifling, that it may be looked upon, in general, as certain that pure clay loses nothing of its weight in the fire; for those trifling diminutions were certainly occasioned by the ferruginous parts which were found in the clay, and which were in part destroyed by the fire. It is also worthy of observation, that the duration of heat in different matters exposed to the same fire for an equal time, is always in the same proportion, whether the degree of heat be greater or smaller.

I have made similar experiments on globes of marble, stone, lead, and tin, by a heat only strong enough to melt tin, and I found, that iron refrigerated in eighteen minutes, so as to be able to hold it in the hand, marble refrigerated to the same degree in twelve minutes, stone in eleven, lead in nine, and tin in eight. It is not, therefore, in proportion to their density, as is commonly supposed, that bodies receive and lose more or less heat, but in an inverse ratio of their solidity; that is, of their greater or lesser _non fluidity_; so that, by the same heat, less time is requisite to heat or cool the most dense fluid.

To prevent the suspicion of vainly dwelling upon assertion, I think it necessary to remark upon what foundation I build this theory; I have found that bodies which should heat in ratio of their diameters, could be only those which were perfectly permeable to heat, and would heat or cool in the same time; hence, I concluded that fluids, whose parts are only held together by a slight connection, might approach nearer to this perfect permeability than solids, whose parts have more cohesion. In consequence of this, I made experiments, by which I found, that with the same heat all fluids, however dense they might be, heat and cool more readily than any solids, however light, so that mercury, for example, heats much more readily than wood, although it be fifteen or sixteen times more dense.

This made me perceive that the progress of heat in bodies cannot, in any case, be made relatively to their density; and I have found by experience, that this progress, as well in solids as fluids, is made rather by reason of their fluidity, or in an inverse ratio of their solidity. I mean by _solidity_ the quality opposite to fluidity; and I say, that it is in an inverse ratio of this quality that the progress of heat is made in both bodies; and that they heat or cool so much the faster as they are the more fluid, and so much the slower as they are more solid, every other circumstance being equal.

To prove that solidity, taken in this sense, is perfectly independent of density, I have found, by experience, that the most or least dense matters, heat or cool more readily than other more or less dense matters, for example, gold or lead, which are much more dense than iron and copper, heat and cool much quicker; while tin and marble, which are not so dense, heat and cool much faster than iron and copper; and there are likewise many other matters which come under the same description; so that density is in no manner relative to the scale of the progress of heat in solid bodies.

It is likewise the same in fluids, for I have observed, that quicksilver, which is thirteen or fourteen times more dense than water, nevertheless heats and cools in less time than water; and spirit of wine, which is less dense than water, heats and cools much quicker; so that generally the progress of heat in bodies, as well with regard to the ingress as egress, has no affinity with their density, and is principally made in the ratio of their fluidity, by extending the fluidity to a solid; from hence I concluded, that we should know the real degree of fluidity in bodies, by heating them to the same heat; for their fluidity would be in a like ratio as that of the time during which they would receive and lose this heat; and that it would be the same with solid bodies. They will be so much the more solid, that is to say, so much the more _non fluids_, as they require more time to receive and lose this heat, and that almost generally to what I presume; for I have already tried these experiments on a great number of different matters, and from them I have made a table, which I have endeavoured to render as complete and exact as possible.

I caused several globes to be made of an inch diameter with the greatest possible precision, from the following matters, which nearly represent the Mineral kingdom.

M. Tillet, of the Academy of Sciences, made the globe of refined gold at my particular request, and the whole of them weighed as follows:

oz. d. gr.

Gold 6 2 17 Lead 3 6 28 Pure silver 3 3 22 Bismuth 3 0 3 Copper-red 2 7 56 Iron 2 5 10 Tin 2 3 48 Antimony melted, and which had small cavities on its surface 2 1 34 Fine 2 1 2 Em 1 2 24-1/2 White marble 1 0 25 Pure clay 0 7 24 Marble common of Montbard 0 7 20 White gypsum, improperly called Alabaster 0 6 36 Calcareous white stone of the quarry of Anieres, near Dijon 6 6 6 Rock chrystal: it was a little too small, and had many defects. I presume that without them it would have weighed 0 6 22 Common glass 0 6 21 Pure earth, very dry 0 6 16 Oker 0 5 9 Porcelain of the Court de Lauraguais 0 5 2-1/2 White chalk 0 4 49 Cherrywood, which although lighter than most other woods, is that which takes in the least fire 0 1 59

I must here observe, that a positive conclusion must not be made of the exact specific weight of each matter from the preceding table, for notwithstanding the precaution that was taken to render the globes equal, yet, as I was obliged to employ different workmen, some were too large, and others too small. Those which were more than an inch diameter were diminished, but those of rock chrystal, glass and porcelain, which were rather too small, we suffered to remain, and only rejected those of agate, jasper, and porphyry, which were sensibly so. This precision in size was however not absolutely necessary, for it could very little alter the result of my experiments.